A construction for binary sequence sets with low peak-to-average power ratio

Parker, Matthew G.; Tellambura, C.

doi:10.1109/isit.2002.1023511

Cited by 18 publications

(31 citation statements)

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“…Our motivation for relating the concept of interlace polynomial to {H, N } n is that this set is related to the Peak-to-Average Power Ratio (PAR) w.r.t. both one and multi-dimensional continuous Discrete Fourier Transforms, and hence to problems in telecommunications and physics for tasks such as channel-sounding, spread-spectrum, and synchronization [19]. We compute Q HN for the clique, line, and clique-line-clique functions.…”

Section: Definitionmentioning

confidence: 99%

One and Two-Variable Interlace Polynomials: A Spectral Interpretation

Riera

Parker

2006

Coding and Cryptography

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Abstract. We relate the one-and two-variable interlace polynomials of a graph to the spectra of a quadratic boolean function with respect to a strategic subset of local unitary transforms. By so doing we establish links between graph theory, cryptography, coding theory, and quantum entanglement. We establish the form of the interlace polynomial for certain functions, provide new one and two-variable interlace polynomials, and propose a generalisation of the interlace polynomial to hypergraphs. We also prove conjectures from [15] and equate certain spectral metrics with various evaluations of the interlace polynomial.

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Section: Definitionmentioning

confidence: 99%

One and Two-Variable Interlace Polynomials: A Spectral Interpretation

Riera

Parker

2006

Coding and Cryptography

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“…The path graph is equivalent to the canonical GRS sequence [5], [20] under lexicographical ordering of the truth table. Table I shows all MMF equivalence classes for Boolean functions of 2 to 5 variables, with inequivalent representatives obtained from [3].…”

Section: A Smallest and Largestmentioning

confidence: 99%

“…It is also clear that high entanglement is indicated by a small sum-of-squares over the joint autocorrelation coefficients, and this can be characterised by the average 1 MMF computed over all subspaces of p(x) obtained by fixing. Finally, although constructions for Golay complementary sequence sets [7] are usually constrained by their univariate aperiodic autocorrelation, they are more naturally constrained by their multivariate aperiodic autocorrelation [20]. For length N = 2 n , Golay-Rudin-Shapiro sequences (GRS) [23], [22] are the only known examples of Golay complementary pairs [7], and their interpretation as certain Reed-Muller, RM(1, m), cosets within RM(2, m) has recently been exploited in [5].…”

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confidence: 99%

“…For length N = 2 n , Golay-Rudin-Shapiro sequences (GRS) [23], [22] are the only known examples of Golay complementary pairs [7], and their interpretation as certain Reed-Muller, RM(1, m), cosets within RM(2, m) has recently been exploited in [5]. This was generalised in [20], which demonstrated the fundamentally multivariate nature of the complementary construction. [11] showed that the MF of the canonical GRS sequence can be computed exactly for any length N = 2 n via the recursion γ n = 2γ n−1 + 8γ n−2 , where γ n is the sum-of-squares for a sequence of length 2 n , leading to an asymptotic MF of 3 for large n. This recursion suggests that other sequence constructions obey similar recursive formulas, both for their univariate and multivariate sum-of-squares, and here we identify many such constructions (see Tables III and IV).…”

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confidence: 99%

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The multivariate merit factor of a Boolean function

Gulliver

Parker

2005

IEEE Information Theory Workshop, 2005.

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Abstract-A new metric, the multivariate merit factor (MMF ) of a Boolean function, is presented, and various infinite recursive quadratic sequence constructions are given for which both univariate and multivariate merit factors can be computed exactly. In some cases these constructions lead to merit factors with non-vanishing asymptotes. A formula for the average value of 1 MMF is derived and a characterisation of the MMF in terms of cryptographic differentials is discussed.

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“…But its upper bounds is not always tight. Another construction based on complementary sets was proposed by Parker and Tellambura [17], [18]. But in generally, the construction does not produce cosets of RM q (1, m).…”

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confidence: 99%

Identify more non-golay complementary sequences for OFDM with low PMEPR using multi-dimensional root pairs

Wang

Zhao

Chen

et al. 2009

2009 Fourth International Conference on Communications and Networking in China

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Abstract-Recently, sub-root pairs and sequences are introduced to identify Davis-Jedwab (DJ) codes, non-Davis-Jedwab (non-DJ) Golay complementary sequences (GCS) and nonGolay complementary sequences (non-GCS) for OFDM with low PMEPR. In this paper, we extend sub-root pairs to superroot pairs. A discrete version of super-root pairs called multidimensional root pairs are used to build arbitrarily interleaving Boolean functions of long length. The newly identified arbitrarily interleaving Boolean functions can produce more non-DJ GCS and non-GCS with PMEPR at most pre-chosen positive number not always being a power of 2. In this way, we propose an efficient method to identify more codes with low PMEPR for OFDM.Index Term-Golay complementary sequences, OFDM, PMEPR, Root pair.In multicarrier communications, the orthogonal frequency division multiplexing (OFDM) has been made use widely. However, a major drawback of OFDM signals is the high peak to mean envelope power ratio (PMEPR) (1, m).Recently, sub-root pairs which is called seed extension in [15] are introduced to identify Davis-Jedwab (DJ)-codes, non-Davis-Jedwab (non-DJ) Golay complementary sequences (GCS) and non-Golay complementary sequences (non-GCS) for OFDM with low PMEPR [12]. However, the binary variables of the sub-root pairs' Boolean function representations can not employ an arbitrarily interleaving pattern with those of DJ-codes. This is a drawback when come to the non-DJ Galay complementary sequences (GCS) which is discovered recently and explained in [8], [9]. In this paper, we generalize subroot pairs to super-root pairs which can be used to construct longer codes with low PMEPR for OFDM by any arbitrarily interleaving patten with DJ-codes. A discrete version of superroot pairs called multi-dimensional root pairs are used to build arbitrarily interleaving Boolean functions of long length, which can identify more non-DJ GCS and non-GCS with PMEPR at most pre-chosen positive number not always being power of 2. In this way, we propose an efficient method to identify more codes with low PMEPR for OFDM. I. NOTATIONS AND PRELIMINARIESBefore proceeding further, let us introduce the OFDM signals, the PMEPR and the related concepts at first. Throughout this paper ξ = exp (2πj/M ), where M is a positive integer. Let an M -ary phase shift keying (MPSK) constellation be denoted by ξ A. OFDM and Power ControlLet j be the imaginary unit, i.e., j 2 = −1. For an MPSK modulation OFDM, let a codeword c = (c 0 , . . . , c n−1 ) with c ∈ ξ Z M , the frequency separation between any two adjacent subcarriers is ∆f = 1/T . Then the n subcarrier complex baseband OFDM signal can be represented aswhere 0 ≤ t < T . The instantaneous power of the complex envelope s c (t) is defined by P c (t) = |s c (t)| 2 .So the peak-to-mean power ratio (PMEPR) of the codeword c is defined by PMEPR(c) = 1 n sup 0≤t

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A construction for binary sequence sets with low peak-to-average power ratio

Cited by 18 publications

References 20 publications

One and Two-Variable Interlace Polynomials: A Spectral Interpretation

One and Two-Variable Interlace Polynomials: A Spectral Interpretation

The multivariate merit factor of a Boolean function

Identify more non-golay complementary sequences for OFDM with low PMEPR using multi-dimensional root pairs

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